Simplify (x^3+x^2-4x-4)/(x^3+2x^2-x-2)

$\frac{x^{3} + x^{2} - 4 x - 4}{x^{3} + 2 x^{2} - x - 2}$

Simplify the numerator.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(x^{3} + x^{2}) - 4 x - 4}{x^{3} + 2 x^{2} - x - 2}$

Factor out the greatest common factor (GCF) from each group.

$\frac{x^{2} (x + 1) - 4 (x + 1)}{x^{3} + 2 x^{2} - x - 2}$

Factor the polynomial by factoring out the greatest common factor, $x + 1$ .

$\frac{(x + 1) (x^{2} - 4)}{x^{3} + 2 x^{2} - x - 2}$

Rewrite $4$ as $2^{2}$ .

$\frac{(x + 1) (x^{2} - 2^{2})}{x^{3} + 2 x^{2} - x - 2}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 2$ .

$\frac{(x + 1) (x + 2) (x - 2)}{x^{3} + 2 x^{2} - x - 2}$

Simplify the denominator.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(x + 1) (x + 2) (x - 2)}{(x^{3} + 2 x^{2}) - x - 2}$

Factor out the greatest common factor (GCF) from each group.

$\frac{(x + 1) (x + 2) (x - 2)}{x^{2} (x + 2) - (x + 2)}$

Factor the polynomial by factoring out the greatest common factor, $x + 2$ .

$\frac{(x + 1) (x + 2) (x - 2)}{(x + 2) (x^{2} - 1)}$

Rewrite $1$ as $1^{2}$ .

$\frac{(x + 1) (x + 2) (x - 2)}{(x + 2) (x^{2} - 1^{2})}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

$\frac{(x + 1) (x + 2) (x - 2)}{(x + 2) (x + 1) (x - 1)}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x + 1$ .

Cancel the common factor.

$\frac{(x + 1) (x + 2) (x - 2)}{(x + 2) (x + 1) (x - 1)}$

Rewrite the expression.

$\frac{(x + 2) (x - 2)}{(x + 2) (x - 1)}$

Cancel the common factor of $x + 2$ .

Cancel the common factor.

$\frac{(x + 2) (x - 2)}{(x + 2) (x - 1)}$

Rewrite the expression.

$\frac{x - 2}{x - 1}$